Abstract
In this paper, for the solution of the continuous algebraic Riccati equation (CARE), we derived two new upper matrix bounds. Compared with the existing results, the newly obtained bounds are less conservative and more practical, which means that the condition for the existence of the upper bounds derived here is much weaker. The advantage of the results is shown by theoretical analysis and numerical examples. Moreover, in redundant optimal control, when we increase the columns of the input matrix, some sufficient conditions are presented to strictly decrease the largest singular value of the feedback matrix by utilizing these upper bounds. We also give some examples to illustrate the effectiveness of these sufficient conditions.
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